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Drona August 3, 2001 07:54

Gravity modelling

Someone in this forum said that you don't need gravity if you are calculating an incompressible, isothermal single phase flow. Is it correct? What about flows under action of gravity(such as flow through a pipe from a high reservoir to a lower level. How to take care of gravity in that case? I understand that some of the commercial CFD codes don't include gravity in momentum equations.

Can someone enlighten me please?


Jan Rusaas August 3, 2001 12:19

Re: Gravity modelling

It is a couple of years ago I graduated, so my memory is probably a bit rusty

I think, the idea is, that Bouyancy is not needed.

The driving force in your example is a pressure difference due to the difference in level.

The correct way to model your example is to include a pressure difference between inlet an outlet, which is equal to the density*level_difference*gravity, (hydrostatic pressure difference - I think is the name)

As in the sea, 10 meter down the pressure is incresed by ca. 1bar 10 meter * 1000 kg/m^3 * 10 m/s^2

So gravity is not needed in the equations in such a case, but is implicit included by the hydrostatic pressure.

Hope it helps (and it is true :) )


Drona August 6, 2001 08:39

Re: Gravity modelling
Dear Jan,

Thanks for the response. My problem is a low head water turbine(total of 2 meter head, 1 meter above runner, one meter below the runner due to draft tube). Now, I am trying to model the whole turbine, from inlet(a pipe leading to scroll casing/vane/runner) and to the outlet(draft tube outlet). To include the pressure difference by boundary conditions, I can only do it by putting inlet and outlet pressures difference of 2 meters because the leve difference is 2 meters. But this doesn't take into consideration where the runner is located. But in actual fact, it may have a big impact, especially cavitation, as long draft tube can introduce cavitation.

I hope I am able to clarify my situation. Do you still think gravity is not needed in this case? When you say Gravity is not needed, are you saying that the rho*g term is not needed in momentum equation as a body force? As a matter of fact, I have to say that I have a very little idea about the mathematical part of the CFD, and I guess John Chien won't like me. What do we mean by buoyancy here, are we talking about the force that is trying to push the turbine upwards?

Sorry for the long message.


Jan Rusås August 6, 2001 09:10

Re: Gravity modelling
Dear Drona,

1) Lets keep Chien out of this. :)

2) It is only neccesary to include bouyancy if the are any difference in density due to pressure or temperature. If any difference in density exist it will result in an additional force which is modelled by including the bouyancy option.

3) I did get a genious idea, I looked in the manual about bouyancy, and found

"Note that there is no need for the gravity vector in non-buoyant flows because the hydrostatic pressure is subtracted out and the program only solves for the reduced pressure"

hmm, not sure if I understand this, but for sure if you do not have any (large) changes in density due to heat transfer or pressure, then there is no need to including gravity.

I think the term on the calculation is (density -ref_density) and if there is only small variation in density then this term is approz. zero

I am a bit confused about what this means for your problem, I guess you must hope that there are some experts in your problem in this forum or as a last solution contact user support. :)


Drona August 6, 2001 10:35

Re: Gravity modelling
Dear Jan,

Only thing I want to say is this: My commercial CFD code gives the same solution for any orientation the turbine has - I mean vertical or horizontal or something else. I am saying this because I don't specify gravity vectors anywhere. Now, for a turbine which runs ON gravity, there should be definitely some significance how you keep the turbine system(about 2 meter long from inlet to outlet) - horizontally or vertically. As of support, help desk did tell me that for approximate solution, I don't need to model gravity, but for accurate results I need to.

That's it for now,


Herve August 7, 2001 05:31

Re: Gravity modelling
Hi Jan, Drona,

The hydrostatic part of pressure is absorbed into the pressure gradient in the r.h.s. of the momentum equation and the code solves for the deviation p'.

Jan Rusås August 7, 2001 06:34

Re: Gravity modelling
Thanks, Herve, for putting some light on this topic.

Does that mean one should not calculate the hydrostatic pressure difference and include it as a pressure difference between inlet and outlet?


Sascha August 10, 2001 07:00

Re: Gravity modelling
For buoyancy-driven flows like water flowing from level one to level two with a certain difference in height you have to include the buoyancy therms in teh momentum equations. THis is in CFX-4 simply done by adding BUOYANCY in the options part...

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